A pilot survey was conducted of $30$ individuals to understand their different attitudes towards discount stores $($e$.$g$.,$ K$-$Mart$),$ which usually come with low levels of service versus departmental stores $($e$.$g$.,$ Macys$)$ which come with higher levels of service. Respondents were asked their opinion on a $0-9$ agree$-$disagree scale $($where $0$ indicates strongly disagree and $9$ indicates strongly agree$)$ on the following questions.

$-$ I never go back to a store that had treated me with disrespect.$($X$1)$

$-$ I find salespeople who fawn over me irritating, I just expect them to courteous.$($X$2)$

$-$ I have a lot of questions when I shop, I greatly appreciate a salesperson who is willing to spend time answering my questions.$($X$3)$

$-$ I care little for the fancy displays in departmental stores.$($X$4)$

$-$ Discount stores are much more of a bargain than departmental stores.$($X$5)$

The data for this study are attached $.$ Answer the following questions $($with relevant tables from SPSS$).$

A$.$ Suppose you were looking to reduce the $5$ variable dataset into $2$ factors. Show the correlation matrix. Based on the correlation matrix of the variables, which variables do you expect to be associated with Factor $1$ and Factor $2.($Note the labels factor$1$ and factor $2$ are arbitrary$).$